Table 1: List of the strongest hydrogen recombination lines studied in this paper. We present the three strongest lines for the first three series of hydrogen atom between excited states: Balmer ( $m\rightarrow 2$ ), Paschen ( $m\rightarrow 3$ ) and Brackett ( $m\rightarrow 4$ ). For each transition $m\rightarrow n$ , we show its name, the rest frame wavelength, and the oscillator strength (these values have been taken from Green et al. 1957). For illustration, we also present in the fifth column the redshifted frequency observed today if emission took place at z=1000. The last column shows the optical depth in the line at that redshift (z=1000), as computed using our code.
Transition m $\lambda_{nm}$ ( $\AA$ ) f_nm $\nu_0(z=1000)$ (GHz) $\tau _{nm}(z=1000)$

Balmer lines (n=2)

H $\alpha$ 3 6562.8 0.6407 456.3 4.53 $\times$ 10^-5

H $\beta$ 4 4861.3 0.1193 616.1 6.14 $\times$ 10^-6

H $\gamma$ 5 4340.5 0.0447 690.0 2.09 $\times$ 10^-6

Paschen lines (n=3)

P $\alpha$ 4 18751.0 0.8421 159.7 1.17 $\times$ 10^-7

P $\beta$ 5 12818.1 0.1506 233.6 1.47 $\times$ 10^-8

P $\gamma$ 6 10938.1 0.0558 273.8 4.75 $\times$ 10^-9

Brackett lines (n=4)

B $\alpha$ 5 40512.0 1.0377 73.9 2.57 $\times$ 10^-8

B $\beta$ 6 26252.0 0.1793 114.1 3.42 $\times$ 10^-9

B $\gamma$ 7 21655.0 0.0655 138.3 1.09 $\times$ 10^-9

**Table 1:** List of the strongest hydrogen recombination lines studied in this paper. We present the three strongest lines for the first three series of hydrogen atom between excited states: Balmer ( $m\rightarrow 2$ ), Paschen ( $m\rightarrow 3$ ) and Brackett ( $m\rightarrow 4$ ). For each transition $m\rightarrow n$ , we show its name, the rest frame wavelength, and the oscillator strength (these values have been taken from Green et al. 1957). For illustration, we also present in the fifth column the redshifted frequency observed today if emission took place at z=1000. The last column shows the optical depth in the line at that redshift (z=1000), as computed using our code.
Transition	m	$\lambda_{nm}$ ( $\AA$ )	f_nm	$\nu_0(z=1000)$ (GHz)	$\tau _{nm}(z=1000)$
Balmer lines (n=2)
H $\alpha$	3	6562.8	0.6407	456.3	4.53 $\times$ 10^-5
H $\beta$	4	4861.3	0.1193	616.1	6.14 $\times$ 10^-6
H $\gamma$	5	4340.5	0.0447	690.0	2.09 $\times$ 10^-6
Paschen lines (n=3)
P $\alpha$	4	18751.0	0.8421	159.7	1.17 $\times$ 10^-7
P $\beta$	5	12818.1	0.1506	233.6	1.47 $\times$ 10^-8
P $\gamma$	6	10938.1	0.0558	273.8	4.75 $\times$ 10^-9
Brackett lines (n=4)
B $\alpha$	5	40512.0	1.0377	73.9	2.57 $\times$ 10^-8
B $\beta$	6	26252.0	0.1793	114.1	3.42 $\times$ 10^-9
B $\gamma$	7	21655.0	0.0655	138.3	1.09 $\times$ 10^-9

Source LaTeX | All tables | In the text

	1 Introduction
	2 Cosmological recombination process
	3 Imprint of hydrogen recombination lines on the CMB
	4 Contamination from other effects
	5 Discussion and conclusions
	References
	Online Material